Berrada Kamal, Bougouffa Smail
Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia.
Entropy (Basel). 2025 Aug 10;27(8):848. doi: 10.3390/e27080848.
In this work, we investigate the quantum coherence and purity in hydrogen atoms under dissipative dynamics, with a focus on the hyperfine structure states arising from the electron-proton spin interaction. Using the Lindblad master equation, we model the time evolution of the density matrix of the system, incorporating both the unitary dynamics driven by the hyperfine Hamiltonian and the dissipative effects due to environmental interactions. Quantum coherence is quantified using the L1 norm and relative entropy measures, while purity is assessed via von Neumann entropy, for initial states, including a maximally entangled Bell state and a separable state. Our results reveal distinct dynamics: for the Bell states, both coherence and purity decay exponentially with a rate proportional to the dissipation parameter, whereas for a kind of separable state, coherence exhibits oscillatory behavior modulated via the hyperfine coupling constant, superimposed on an exponential decay, and accompanied by a steady increase in entropy. Higher dissipation rates accelerate the loss of coherence and the growth of von Neumann entropy, underscoring the environment's role in suppressing quantum superposition and driving the system towards mixed states. These findings enhance our understanding of coherence and purity preservation in atomic systems and offer insights for quantum information applications where robustness against dissipation is critical.
在这项工作中，我们研究了耗散动力学下氢原子中的量子相干性和纯度，重点关注由电子 - 质子自旋相互作用产生的超精细结构态。使用林德布拉德主方程，我们对系统密度矩阵的时间演化进行建模，纳入了由超精细哈密顿量驱动的幺正动力学以及由于环境相互作用引起的耗散效应。对于包括最大纠缠贝尔态和可分态在内的初始态，使用L1范数和相对熵度量来量化量子相干性，通过冯·诺依曼熵来评估纯度。我们的结果揭示了不同的动力学：对于贝尔态，相干性和纯度都以与耗散参数成比例的速率指数衰减，而对于一种可分态，相干性呈现出通过超精细耦合常数调制的振荡行为，叠加在指数衰减之上，并伴随着熵的稳定增加。更高的耗散率加速了相干性的损失和冯·诺依曼熵的增长，突出了环境在抑制量子叠加和驱使系统趋向混合态方面的作用。这些发现加深了我们对原子系统中相干性和纯度保持的理解，并为量子信息应用提供了见解，在这些应用中，对耗散的鲁棒性至关重要。
